Collab.orative Research: DMS NIGMS: Dense life-log health analytics from wearable sensors using functional analysis and Riemannian geometry 1 Introduction The growth and popularity of wearable devices, such as accelerometers, smartphones, and wearable cam-. eras, coupled with larger storage capacities water-proofing, and more unobtrusive wear locations, has 1 transformed long-term monitoring of behaviors (i.e., > 1 week) throughout the 24-hour spectrum. Consumer- based accelerometers (e.g., GENEActiv, Fitbil etc.) are already achieving long-term population-level data collection of movement patterns, allowing us to glean insights and associations with important health out- comes. With the collection of long-term data, it may now be possible to characterize weekly, seasonal, and even annual patterns of behaviors that encapsulate the full 24-hour spectrum that extend beyond tra- ditional methods. The typical wearable device contains several complementary sensors (accelerometers, gyro, heart-rate monitor etc.) and samples al high rates (e.g. lOOHz for accelerometer). Thus, the high- sampling rates and the long capture duration result in life-log data that truly qualifies as multimodal and big time-series data. This is a highly interdisciplinary project that will advance and adapt fundamental mathematical and sta- tistical techniques towards making breakthrough progress in analysis of life-log data. This research project is ideally suited for this NSF-NIH program by identifying critical mathematical and statistical problems in the analysis of dense life-log data. We also develop im10vative mathematical and statistical frameworks needed lo solve the emergent problems in this endeavor. We first start by motivating how big life-log data can revolutionize health-care practices, what computational barriers exist to realize the vision, and how we propose to overcome those. Insights de1ived from life-log data. We consider the following motivating application examples to make our case, and then motivate the use of the proposed mathematical tools. The existence of periodicities in human behavior is related to the rest-activity cycle that can represent the human circadian system. Disruptions in the circadian system consistently show profound and detrimental impacts on health [1] and studies using accelerometry have shown relationships with health-related quality of life with better survival following metastatic colorectal cancer chemotherapy treatments [2, 3]. In a mathematical sense, periodicities, or the lack of periodicity, and the strength of periodicity more generally, can be precisely quantified with the new mathematical methods drawn from functional data-analysis, and dynamical modeling, and made further scalable via effective algo- rithmic approximation strategies. A study may aim to increase in-home physical activity and energy expenditure post-stroke by in- creased time spent in walking. But ii may turn out that the goal of energy expenditure may still be met, despite low levels of the activity of interest, because the participant engages in a different activ- ity (e.g. swimming, dusting, yard-work). These different activities may differ significantly in signal- statistics from the activity prescribed, but may achieve similar outcomes. It is not feasible to a-priori decide all possible physical activities, so the challenge is to discover relevant activity classes from raw life-log data, for which signal models may not be available a-priori. The tools proposed herein will allow effective discovery cif significant recurring patterns from low-level signal data, which may lead to more personalized interventions to be designed by clinici~ns. Physical attributes, such as heart rate and body temperature, reflect one's health status but are also influenced by context and differ from one individual to another. For example, occasional heart ar- rhythmias may indicate serious problems, but can also be caused by various activities [4]. With conventional medical practice, arrhythmias might only be discovered during a routine examination at the doctor's office, and further monitoring requires special devices and a self-maintained diary of daily activities [4]. This could lead lo omissions and inaccuracies. Multi-modal life-log data enables re-examination of statistical attributes of correlated time-series data so that we can develop tools_ for 1nore accurate, context-aware, and personal~zed discovery of individual patterns. Challenges posed by life-log big-data: Some of the challenges, and our proposed approach lo tackle the problems that arise in the above endeavor are as follows: 1 1902582